Isogeometric analysis on implicit domains using weighted extended PHT-splines

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:350

Article

Qarariyah, Ammar¹  Deng, Fang²  Yang, Tianhui¹  Liu, Yuan³  Deng, Jiansong¹ 

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[2] North China Univ Water Resources & Elect Power, Sch Math & Stat, Zhengzhou 450045, Henan, Peoples R China

[3] Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China

关键词: Isogeometric analysis;    WEB method;    PHT-splines;    Weight function;   

DOI  :  10.1016/j.cam.2018.10.012

来源: Elsevier

【 摘 要 】

The urging quest for diminishing the gap between finite element methods and computer aided design is growing every day. Isogeometric analysis is driving that search a step forward in contrast with traditional finite element methods. One of the areas that need more investigation is using isogeometric analysis on domains that contain singularities. In this case, the parameterization process is occasionally non-trivial, and some of the inherited basis functions are not well defined producing rough solutions. Moreover, NURBS basis functions are not the best choice to perform local refinement since adaptivity is indispensable. In this study, a new approach that serves as a generalization for some of the ideas in both the isogeometric analysis and the WEB method is introduced. Isogeometric analysis on implicit domains replaces mesh generation with implicit spline weight function generation and construct weighted extended PHT-splines for analysis. The geometry and the analysis both are built starting from the same function space avoiding parameterization. The PHT-splines are adaptive and allow local refinement naturally leading to a higher accuracy while dealing with singularities. An illustration with numerical examples demonstrates the efficiency and performance of the proposed method. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free